Chapter 5.2, Problem 32E

(a)

To determine

To find: the line of intersection

Answer to Problem 32E

Hence, the lines appear to intersect is $\left(4,5\right)$

Explanation of Solution

Given:

  

Calculation:

From the graph, it is clear that the lines meet at $\left(4,5\right)$

Conclusion:

Hence, the lines appear to intersect is $\left(4,5\right)$

(b)

To determine

To solve: a system of linear equations to check the answer found in part(a)

Answer to Problem 32E

Hence,the solution is indeed $\left(4,5\right)$

Explanation of Solution

Given: The graphs of two linear equations are shown.

  

Calculation:

Yes, Substitute $y=x+1$ to the other equation:

  $\begin{array}{l}x+1=6-\frac{1}{4}x\leftarrow \text{Solve for x}\\ \frac{5}{4}x=5\leftarrow \text{Divide by }\frac{5}{4}\\ x=4\end{array}$

Solve for $y$ :

  $\begin{array}{l}y=4+1\\ y=5\end{array}$

The solution is indeed $\left(4,5\right)$

Conclusion:

Hence,the solution is indeed $\left(4,5\right)$